Problem: Simplify the following expression: $ t = \dfrac{-7}{4} + \dfrac{-k - 9}{k - 3} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{k - 3}{k - 3}$ $ \dfrac{-7}{4} \times \dfrac{k - 3}{k - 3} = \dfrac{-7k + 21}{4k - 12} $ Multiply the second expression by $\dfrac{4}{4}$ $ \dfrac{-k - 9}{k - 3} \times \dfrac{4}{4} = \dfrac{-4k - 36}{4k - 12} $ Therefore $ t = \dfrac{-7k + 21}{4k - 12} + \dfrac{-4k - 36}{4k - 12} $ Now the expressions have the same denominator we can simply add the numerators: $t = \dfrac{-7k + 21 - 4k - 36}{4k - 12} $ $t = \dfrac{-11k - 15}{4k - 12}$